Wednesday, December 31

Wednesday, December 24

Eric Angelini suggested on Monday the sequence of numbers with the property that if one inserts a single plus anywhere inside them (and executes the additions) only primes result. In deference to the second part of the number-split not starting with it, he only allowed zero as a final digit:

Surely this sequence is finite. But what is the largest term? My program hinted that it might be the 11-digit 46884486265 (term #440), since it found no 12-digit representative. But (thankfully) I had the computation plod on:

All prime! By plugging 5391391551358 into Google, I discovered that this number was already known to Giovanni Resta, who treated the sequence from the perspective of allowing internal zeros. The numbers 20, 101, and 1001 appear to be (currently) missing from his magnanimous numbers list. But, he has one larger example: